CamCASP/Bugs/7

CamCASP => Bugs => Polarizabilities

Most of the polarizabilities generated by CamCASP show the expected monotonic decrease with increasing imaginary frequency. A few, however, depart wildly from this behaviour. In the example case of formamide, we get, for C,

20 20
            3.74300000      3.98200000      5.26700000      8.33300000 +++
           11.43900000     11.41700000      7.41600000      2.64700000 +++
            0.42400000      0.01400000

with similar behaviour for C 11c 20, C 22c 22s and O 11c 20, but none of the other cases. Removing the "options tests" line from the data to get the standard grid makes things even worse:

20 20
           -9.88200000     -9.52700000     -7.58300000     -2.61900000 +++
            3.70900000      7.16600000      5.79900000      2.32900000 +++
            0.39500000      0.01400000

This is a problem with pfit; the anchor values are

           33.27220340     33.16682559     32.53705396     30.41159247 +++
           25.60290131     18.22199084     10.00593354      3.58000511 +++
            0.63051681      0.02341723

Weight 5 improves matters, but weight 6 is needed to get sensible results: 20 20

           20.80100000     20.83700000     20.99700000     21.01100000 +++
           19.14900000     14.68600000      8.43300000      2.77400000 +++
            0.39500000      0.01400000

The fit is still pretty good: r.m.s. error 0.073% for weight 6 compared with 0.042% for weight 4. Even with weight 6 there are some anomalous cases, especially O 20 20, but the absolute values are small.

Later: I realise that the off-diagonal components of the polarizability don't have to decrease monotonically -- the numerators in the sum-over-states expression may have different signs and decay at different rates. However the diagonal ones should be positive everywhere and should decay monotonically.

I'm exploring the frequency behaviour of the unrefined polarizabilities. It may be possible to represent them by pseudo-DOSD expressions with just a few terms -- maybe only one -- in which case pfit could be modified to fit the parameters in those expressions rather than the individual values.